My kids started doing it under supervision at around 4, but I still washed their hair. At around 6, they started washing their own hair, and I just go in to make sure the shampoo is rinsed out properly

My just turned 3 year old washes himself (not hair), but being a male I don't have to make sure private parts are cleaned good. My just turned 5 year old, DD, washes herself but I wash her hair. Both are with me there. DD is starting to like her privacy though.

When mine turned 4&6 they no longer wanted to bath together, so we let ods use the guest bedroom shower stall style shower while yds stilled took a bath. At age 4 he bathed himself but I was in the room just in case but usually on my iPad or cleaning the bathroom.
By 4.5 he started to shower and both were showering and I just check hair to make sure all the shampoo is out.

My son insists to bathe himself. He just turned 3. He gets a little cup of soap, a wash rag, some toys and about 2 inches of water. Once he's ready to get out he asks for the shower to be turned on so he can rinse.